Advertisements
Advertisements
प्रश्न
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Advertisements
उत्तर
Let the points be A(a, b + c), B(b, c + a) and C(c, a + b)
Area of the triangle = `1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]`
= `1/2["a"("c" + "a") + "b"("a" + "b") + "c"("b" + "c") - "b"("b" + "c") + "c"("c" + "a") + "a"("a" + "b")]`
= `1/2["ac" + "a"^2 + "ab" + "b"^2 + "bc" + "c"^2 - ("b"^2 + "bc" + "c"^2 + "ac" + "a"^2 + "ab")]`
= `1/2 xx 0`
= 0
Since the area of a triangle is 0.
∴ The given points are collinear.
APPEARS IN
संबंधित प्रश्न
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
A hand fan is made by stitching lo equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.
A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied
Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m
Find the area of an equilateral triangle whose perimeter is 180 cm
Find the area of the unshaded region
An isosceles right triangle has area 8 cm2. The length of its hypotenuse is ______.
A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
